Preprint 2007-030

On admissibility criteria for weak solutions of the Euler equations

Camillo De Lellis and László Székelyhidi

Abstract:
We consider solutions to the Cauchy problem
for the incompressible Euler equations
satisfying several additional requirements,
like the global and local energy inequalities.
Using some techniques introduced in an earlier paper we
show that, for some bounded compactly supported initial
data, none of these admissibility criteria singles out a
unique weak solution.

As a byproduct we show bounded initial data
for which admissible solutions to the p-system
of isentropic gas dynamics in Eulerian coordinates
are not unique in more than one space dimension.

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